Unsteady aeroelastic optimization in the transonic regime
Abstract
A methodology for including transonic flutter requirements into the preliminary automated structural design environment is developed and tested. The problem of minimizing structural weight while satisfying behavioral constraints is stated in nonlinear mathematical programming form and is solved using a gradient-based optimization technique. The structure is modeled using finite elements and the associated design variables consist of the structural properties; thicknesses of skins, spars, and ribs, cross-sectional areas of spar and rib caps, and concentrated masses. The method requires that the transonic unsteady aerodynamic forces be represented in the frequency or Laplace domain. In this work the Indicial Response Method is used to transform the time domain aerodynamic forces found by solving the Transonic Small Disturbance equations into the Laplace domain. The indicial responses are calculated about static aeroelastic equilibriums found using the Transonic Small Disturbance equations for the steady aerodynamics. Once in the Laplace domain the unsteady aerodynamic forces are used to determine system dynamic stability by the p-method and to develop semi-analytic equations for the flutter constraint sensitivities. With constraint values and the required gradients, a Taylor Series Approximation is used to develop an approximate nonlinear mathematical programming problem for weight minimization. This approximate optimization problem is iteratively solved by the Method of Modified Feasible Directions until convergence of the exact problem is obtained. Examples of the redesign methodology are given for the simultaneous consideration of constraints on transonic flutter, stresses, and displacements. Results found using nonlinear aerodynamics show that designs can differ considerably from those obtained using linear unsteady aerodynamics when in the transonic flight regime.
Degree
Ph.D.
Advisors
Yang, Purdue University.
Subject Area
Aerospace materials
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